This invention relates to the fields of electronic spectrum analysis and methods and circuits used to perform calculations and approximations of trigonometric functions, and more particularly to methods and circuits for determining the phase angle of a complex electrical signal in a spectrum analysis instrument.
A spectrum analyzer is an electronic instrument for providing a frequency domain view of an electrical signal. In a digital spectrum analyzer, a series of amplitude measurements of the signal under analysis are made over time and the values measured are converted to digital words. This stream of digital words representing amplitude values of the signal over a series of times is information in the time domain. A Fourier transform of this time domain information produces a frequency domain description of the same information. This frequency domain description of the electronic signal under analysis can be displayed to an operator as a graph of power amplitude versus frequency, allowing the operator to analyze the signal's spectral content.
In a digital spectrum analyzer continuously monitoring a wideband spectrum, a large number of phase angle calculations must be performed very rapidly. When a complex electrical signal has been characterized by a pair of data sets representing the in-phase and quadrature components of that signal over time, the phase angle of the signal as a function of time may be calculated by taking the arctangent of the quotient of the two values that describe the signal at each point: EQU phase(t)=arctan[y(t)/x(t)],
where x(t) is the in-phase component of the signal,
and y(t) is the quadrature component of the signal.
However, in a digital computer, division is a rather cumbersome and time consuming operation which it is desirable to avoid if alternative methods are available. Similarly, known techniques for taking the arctangent of a quantity also involve cumbersome calculations or lookups from an extensive table or a combination of lookups and interpolation calculations. What is desired is a method for simplifying the determination of phase angle, so that many of these determinations can be accomplished quickly enough to provide realtime phase information for a high speed digital spectrum analyzer monitoring a wide bandwidth continuously.